function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%

% Part1: cost
one_X = [ones(m,1) X]; % X:5000*401 Theta1:25*401 Theta2:10*26
h = sigmoid(one_X*Theta1'); % 5000*25
h = [ones(size(h,1), 1) h]; % 5000*26
h = sigmoid(h*Theta2'); % 5000*10
yMat = zeros(m, num_labels);
for i = 1:m
    yMat(i, y(i)) = 1;
end

% fprintf('\n yMat row: %d', size(yMat, 1));
% fprintf('\n yMat col: %d', size(yMat, 2));
% fprintf('\n h row: %d', size(h, 1));
% fprintf('\n h col: %d\n', size(h, 2));

J = -1/m*sum(sum(yMat.*log(h) + (1-yMat).*log(1-h))) + lambda/2/m*(sum(sum(Theta1(:,2:input_layer_size+1).^2))+sum(sum(Theta2(:,2:hidden_layer_size+1).^2)));
debug = 0;
% Part 2: backpropagation
for i = 1:m
    a1 = one_X(i, :)';  % 401x1
    z2 = Theta1 * a1;   % 25x1
    a2 = [1; sigmoid(z2)]; % 26x1
    z3 = Theta2 * a2;   % 10x1
    a3 = sigmoid(z3);   % 10x1
    yVec = ([1:num_labels]==y(i))';
    delta_3 = a3 - yVec;
    delta_2 = Theta2' * delta_3 .* (a2 .* (1 - a2)); % 26x1
    % delta_2 = Theta2' * delta_3 .* [1; sigmoidGradient(z2)]; % 26x1
    delta_2 = delta_2(2:end);   % 25x1
    
    Theta1_grad += delta_2 * a1';
    Theta2_grad += delta_3 * a2';
end

Theta1_grad /= m;
Theta1_grad(:, 2:end) += lambda/m * Theta1(:, 2:end);
Theta2_grad /= m;
Theta2_grad(:, 2:end) += lambda/m * Theta2(:, 2:end);

% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
